?cos(?x)dx please help, it would be greatly appreciated if anyone could help! thanks!
A alexa_xox New member Joined Jan 23, 2009 Messages 7 Jan 28, 2009 #1 ?cos(?x)dx please help, it would be greatly appreciated if anyone could help! thanks!
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Jan 28, 2009 #2 Integration by parts is a good way to approach this one. ∫cos(x)dx\displaystyle \int cos(\sqrt{x})dx∫cos(x)dx Let v=sin(x), du=1xdx, u=2x, du=1xdx\displaystyle v=sin(\sqrt{x}), \;\ du=\frac{1}{\sqrt{x}}dx, \;\ u=2\sqrt{x}, \;\ du=\frac{1}{\sqrt{x}}dxv=sin(x), du=x1dx, u=2x, du=x1dx 2xsin(x)−∫sin(x)xdx\displaystyle 2\sqrt{x}sin(\sqrt{x})-\int\frac{sin(\sqrt{x})}{\sqrt{x}}dx2xsin(x)−∫xsin(x)dx Use a u sub on the integral remaining and finish.
Integration by parts is a good way to approach this one. ∫cos(x)dx\displaystyle \int cos(\sqrt{x})dx∫cos(x)dx Let v=sin(x), du=1xdx, u=2x, du=1xdx\displaystyle v=sin(\sqrt{x}), \;\ du=\frac{1}{\sqrt{x}}dx, \;\ u=2\sqrt{x}, \;\ du=\frac{1}{\sqrt{x}}dxv=sin(x), du=x1dx, u=2x, du=x1dx 2xsin(x)−∫sin(x)xdx\displaystyle 2\sqrt{x}sin(\sqrt{x})-\int\frac{sin(\sqrt{x})}{\sqrt{x}}dx2xsin(x)−∫xsin(x)dx Use a u sub on the integral remaining and finish.
A alexa_xox New member Joined Jan 23, 2009 Messages 7 Jan 28, 2009 #3 thank you so much! that has helped immensely!!
